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Definition of Functions

If α and ...

Question

If $α$ and $β$ are the zeroes of the polynomial $f (x) = a x^{2} + b x + c$ , then Find $\frac{1}{α^{2}} + \frac{1}{β^{2}}$ .

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Solution

$\frac{1}{α^{2}} + \frac{1}{β^{2}} = \frac{α^{2} + β^{2}}{{(α β)}^{2}} = \frac{{(α + β)}^{2} - 2 α β}{{(α β)}^{2}} = \frac{\frac{b^{2}}{a^{2}} - \frac{2 c}{a}}{\frac{c^{2}}{a^{2}}} = \frac{b^{2} - 2 a c}{a^{2}} \times \frac{a^{2}}{c^{2}} = \frac{b^{2}}{c^{2}} - \frac{2 a}{c}$

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Similar questions

α, β

are the zeros of the polynomial

f (x) = a x^{2} + b x + c

\frac{1}{α^{2}} + \frac{1}{β^{2}}

α

β

are the zeros of the quadratic polynomial

f (x) = a x^{2} + b x + c

, then evaluate:

α^{2} β + α β^{2}

α, β

are zeroes of the quadratic polynomial

a x^{2} + b x + c

then find the value of

α^{2} - β^{2}

Q. If α, β are the zeros of the polynomial ax² + bx + c, then (α² + β²) = ?

(a)

\frac{a^{2} - 2 b c}{b^{2}}

\frac{b^{2} - 2 a c}{a^{2}}

\frac{a^{2} + 2 b c}{b^{2}}

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α

β

be the zeros of

f (x) = a x^{2} + b x + c, a \neq 0

Δ = b^{2} - 4 a c

α + β, α^{2} + β^{2}

α^{3} + β^{3}

are in G.P., then :

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